Siri matches these phrases exactly, so they are printed here rather than left to guess. Close is not close enough: "my Sigma total" is not one of them and Siri will offer to search the web instead of asking what you meant.
TODAY'S TOTAL: "What's my Sigma total", "Sigma total", "What did I eat in Sigma", "How much have I eaten in Sigma".
LOG A FOOD: "Log a food in Sigma", "Log food in Sigma", "Add a food to Sigma". It asks which food, from the ones you have.
LOG A SPOKEN MEAL: "Log a meal in Sigma", "Tell Sigma what I ate". Then say the meal, and it estimates each item.
None of these open the app. The phone can stay in your pocket.
For the fastest version, bind Log a Food to the Action Button: Settings, Action Button, Shortcut, Sigma. One press, no talking. Every one of these also appears in the Shortcuts app if you'd rather build your own.
One catch worth knowing: Siri registers these phrases per language, and Sigma's exist in English only. If Siri speaks something else, it has no Sigma phrases at all and will offer to search the web. Siri's language is a separate setting from the phone's.